sklearn.linear_model.orthogonal_mp_gram
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sklearn.linear_model.orthogonal_mp_gram(Gram, Xy, n_nonzero_coefs=None, tol=None, norms_squared=None, copy_Gram=True, copy_Xy=True, return_path=False, return_n_iter=False)
[source]
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Gram Orthogonal Matching Pursuit (OMP)
Solves n_targets Orthogonal Matching Pursuit problems using only the Gram matrix X.T * X and the product X.T * y.
Read more in the User Guide.
Parameters: |
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Gram : array, shape (n_features, n_features) -
Gram matrix of the input data: X.T * X -
Xy : array, shape (n_features,) or (n_features, n_targets) -
Input targets multiplied by X: X.T * y -
n_nonzero_coefs : int -
Desired number of non-zero entries in the solution. If None (by default) this value is set to 10% of n_features. -
tol : float -
Maximum norm of the residual. If not None, overrides n_nonzero_coefs. -
norms_squared : array-like, shape (n_targets,) -
Squared L2 norms of the lines of y. Required if tol is not None. -
copy_Gram : bool, optional -
Whether the gram matrix must be copied by the algorithm. A false value is only helpful if it is already Fortran-ordered, otherwise a copy is made anyway. -
copy_Xy : bool, optional -
Whether the covariance vector Xy must be copied by the algorithm. If False, it may be overwritten. -
return_path : bool, optional. Default: False -
Whether to return every value of the nonzero coefficients along the forward path. Useful for cross-validation. -
return_n_iter : bool, optional default False -
Whether or not to return the number of iterations. |
Returns: |
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coef : array, shape (n_features,) or (n_features, n_targets) -
Coefficients of the OMP solution. If return_path=True , this contains the whole coefficient path. In this case its shape is (n_features, n_features) or (n_features, n_targets, n_features) and iterating over the last axis yields coefficients in increasing order of active features. -
n_iters : array-like or int -
Number of active features across every target. Returned only if return_n_iter is set to True. |
Notes
Orthogonal matching pursuit was introduced in G. Mallat, Z. Zhang, Matching pursuits with time-frequency dictionaries, IEEE Transactions on Signal Processing, Vol. 41, No. 12. (December 1993), pp. 3397-3415. (http://blanche.polytechnique.fr/~mallat/papiers/MallatPursuit93.pdf)
This implementation is based on Rubinstein, R., Zibulevsky, M. and Elad, M., Efficient Implementation of the K-SVD Algorithm using Batch Orthogonal Matching Pursuit Technical Report - CS Technion, April 2008. http://www.cs.technion.ac.il/~ronrubin/Publications/KSVD-OMP-v2.pdf